Physics HL · Chapter 18: Electric and Magnetic Fields
18.2 Magnetic Forces on Moving Charges and Currents
Apply Lorentz-force geometry and current-force formulas, then connect to force-per-length behavior for parallel currents.
Estimated time: 38 minutes
Lorentz Force on a Moving Charge
A magnetic field exerts force only on moving charge. The force is perpendicular to both velocity and magnetic field, so magnetic force changes direction of velocity more naturally than speed (in ideal no-electric-field cases). If velocity is parallel or antiparallel to field, force is zero.
F = |q|vBsin heta,qquad ec{F}=q, ec{v} imes ec{B}
theta is the angle between velocity and field vectors; direction follows right-hand rule for positive charge and reverses for negative charge.
Because force is always perpendicular to velocity in a uniform magnetic field, ideal motion with v perpendicular to B becomes circular. This is one reason magnetic fields are used to steer beams in accelerators and mass analyzers. Energy can remain constant while path curvature changes.
Force on a Current-Carrying Wire
A current is moving charge, so a wire segment inside a magnetic field feels a magnetic force. Direction again is perpendicular to current direction and field direction. Treating current as moving charges gives intuition, while the wire formula gives calculation speed.
L is the length of wire segment inside the field region.
Parallel Currents: Attraction and Repulsion
Two long parallel currents interact through each other's magnetic fields. Parallel currents attract; anti-parallel currents repel. This result feels less mysterious if you draw each wire's local field direction at the other wire and apply F = BIL direction logic step by step.
rac{F}{L}= rac{mu_0 I_1 I_2}{2pi r}
Useful for long-wire force-per-unit-length calculations.
Note
When force direction is the goal, solve geometry first and postpone arithmetic. Direction errors are rarely fixed by cleaner arithmetic later.
Simulation: Lorentz-Force Direction Lab
Adjust velocity angle, charge sign, and magnetic-field direction to see how Lorentz-force direction rotates and reverses.
B around wire
1.20e-5 T
Probe location
-7.1 cm, 7.1 cm
|Fm| = |q|vB
0.01 N
Force direction
115.0 deg
Test Yourself
A +3.0 microC charge moves at 2.0 x 10^5 m/s perpendicular to a 0.40 T field. Enter the magnetic-force magnitude.
Hint: Use F = qvB with sin(theta) = 1.